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random(Type) -- random element of a type

Synopsis

Description

Synopsis

  • Usage:
    random T
  • Inputs:
  • Outputs:
    • a random instance of the type T. If the Height option specifies a number h and T is ZZ and , then the integers returned are in the range 0 .. h-1; for QQ the numerator and denominator are in the range 1 .. h.
i1 : random RR

o1 = .540668544119264

o1 : RR (of precision 53)
i2 : random CC_100

o2 = .161092593538603138747300046387+.822484319017049371809468398385*ii

o2 : CC (of precision 100)
i3 : tally for i to 100 list random GF 11

o3 = Tally{-1 => 12}
           -2 => 13
           -3 => 9
           -4 => 8
           -5 => 7
           0 => 9
           1 => 10
           2 => 8
           3 => 4
           4 => 12
           5 => 9

o3 : Tally
i4 : random GF(2,40)

      38    37    36    35    32    31    30    28    27    21    17    14  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      13    12    11    10    8    7    6    3    2
     a   + a   + a   + a   + a  + a  + a  + a  + a

o4 : GF 1099511627776

Synopsis

  • Usage:
    random(d,R)
  • Inputs:
  • Outputs:
    • a random homogeneous element of the ring R of degree d
i5 : R = ZZ[x,y];
i6 : random(5,R)

       5     4      3 2     2 3       4     5
o6 = 3x  + 8x y + 4x y  + 2x y  + 8x*y  + 5y

o6 : R
i7 : R = GF(25,Variable=>a)[x,y];
i8 : VerticalList for i to 6 list random(3,R)

     { 3      2                2     3                     }
o8 = {x  + a*x y + (- a - 1)x*y  + 2y                      }
     {           3            2          2     3           }
     {(- 2a - 2)x  + (2a - 2)x y + 2a*x*y  + 2y            }
     {           3           2          2           3      }
     {(- 2a - 2)x  + (a - 2)x y - 2a*x*y  + (a - 2)y       }
     {          3            2       2              3      }
     {(- a + 2)x  + (2a - 2)x y - x*y  + (- 2a + 1)y       }
     {        3             2                 2           3}
     {(a + 1)x  + (- a - 1)x y + (- 2a - 2)x*y  + (a + 1)y }
     {        3            3                               }
     {(a - 2)x  + (2a - 1)y                                }
     {          3              2         2           3     }
     {(- a - 2)x  + (- 2a + 2)x y + a*x*y  + (a - 1)y      }

o8 : VerticalList
The length of d, if it's a list, should be the same as degreeLength R.

See also